In response to the following example which I posted:>> Consider the mayor of Ashtabula. Let A = "mayor's right eye is blue". >> Let B = "mayor's left eye is blue". Let B' = "mayor's left eye is brown". >> What do you suppose is the truth value of A B ? What about A B' ? >> >> The difficulty is that rules of the kind applied in fuzzy logic >> ignore relations between the elements of a compound proposition.
"Earl Cox" <earldcox1@home.com> wrote:> [...] I also fail to see how your example about the eye color > addresses anything about fuzzy logic.
I see that I left too much implied. The truth values of B and B' in the example above are more or less equal; I don't think you'll want to argue that point. Yet then the truth values assigned to the compound propositions "A and B" and "A and B'" would have to be similar also, under the truth(A and B) = min(truth(A), truth(B)) or truth(A)*truth(B), or any other definition of truth(A and B) which is solely a function of truth(A) and truth(B).> And why do you suppose (erroneously) that fuzzy logic -- fuzzy set theory > in particular -- ignores relationships between compound propositions??
Well, it's from reading introductions to fuzzy logic that give definitions of the truth value of a compound proposition in terms of truth values of its elements. Any such definition must ignore the relation between elements in a compound: if truth(B')=truth(B), then in any proposition containing A and B, I can swap in B' in place of B, and get exactly the same truth value for the compound; whether the elements are redundant, contradictory, or completely unrelated doesn't enter the calculation. Regards, Robert Dodier -- "Nature exists once only." -- Ernst Mach